The Conformal Group of a Conformally Flat Space Time and Its Twistor Representations
Chapter
Abstract
Let (M,g) and (’M,’g) be two D-dimensional real pseudo-Riemannian manifolds, whose metric tensors g and ‘g have the same signature. A diffeomorphism φ: U →’U of a neighbourhood U ⊂M onto ‘U⊂’M is said to be conformal if the corresponding tangent map φT preserves the angles. In a slightly more technical language this means that for given coordinates Xµ and ’Xµ on U and ’U we have
$$\frac{{\partial \varphi _{(x)}^\kappa }}{{\partial {x^\mu }}}\frac{{\partial \varphi _{(x)}^\lambda }}{{\partial {x^\nu }}}'{g_{\kappa \lambda }}(\varphi (x)) = {\Omega ^2}(x){g_{\mu \nu }}(x)(\Omega > 0).$$
(1.1)
Keywords
Minkowski Space Conformal Transformation Conformal Group Twistor Representation Causal Order
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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© Springer-Verlag Berlin Heidelberg 1986